Linear Optimization Problems with Inexact Data / Edition 1

by Miroslav Fiedler, Josef Nedoma, Jaroslav Ramik, Jiri Rohn, Karel Zimmermann

Overview

Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems—for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average" values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the shastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Product Details

ISBN-13:	9781441940940
Publisher:	Springer US
Publication date:	10/29/2010
Edition description:	Softcover reprint of hardcover 1st ed. 2006
Pages:	214
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Matrices.- Solvability of systems of interval linear equations and inequalities.- Interval linear programming.- Linear programming with set coefficients.- Fuzzy linear optimization.- Interval linear systems and optimization problems over max-algebras.

Editorial Reviews

From the reviews:

"The authors have recollected here their results that were published in various journals, research reports and proceedings, mainly between 1994 and 2000. … This research monograph is aimed at the audience interested in optimization, operations research, linear algebra and fuzzy sets." (S. Zlobec, Mathematical Reviews, Issue 2007 b)

From the Publisher